Solve sqrt{2*16595.84/3*3600*66*3.14*8}

$$\sqrt{ \frac{ 2 \cdot 16595.84 }{ 3 \cdot 3600 \cdot 66 \cdot 3.14 \cdot 8 } }$$

Evaluate

$$\frac{\sqrt{44782837}}{155430}\approx 0.043054738$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\sqrt{\frac{16595.84}{3\times 3.14\times 8\times 66\times 1800}}$$

Multiply 3 and 3.14 to get 9.42.

$$\sqrt{\frac{16595.84}{9.42\times 8\times 66\times 1800}}$$

Multiply 9.42 and 8 to get 75.36.

$$\sqrt{\frac{16595.84}{75.36\times 66\times 1800}}$$

Multiply 75.36 and 66 to get 4973.76.

$$\sqrt{\frac{16595.84}{4973.76\times 1800}}$$

Multiply 4973.76 and 1800 to get 8952768.

$$\sqrt{\frac{16595.84}{8952768}}$$

Expand \frac{16595.84}{8952768} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1659584}{895276800}}$$

Reduce the fraction \frac{1659584}{895276800} to lowest terms by extracting and canceling out 64.

$$\sqrt{\frac{25931}{13988700}}$$

Rewrite the square root of the division \sqrt{\frac{25931}{13988700}} as the division of square roots \frac{\sqrt{25931}}{\sqrt{13988700}}.

$$\frac{\sqrt{25931}}{\sqrt{13988700}}$$

Factor 13988700=90^{2}\times 1727. Rewrite the square root of the product \sqrt{90^{2}\times 1727} as the product of square roots \sqrt{90^{2}}\sqrt{1727}. Take the square root of 90^{2}.

$$\frac{\sqrt{25931}}{90\sqrt{1727}}$$

Rationalize the denominator of \frac{\sqrt{25931}}{90\sqrt{1727}} by multiplying numerator and denominator by \sqrt{1727}.

$$\frac{\sqrt{25931}\sqrt{1727}}{90\left(\sqrt{1727}\right)^{2}}$$

The square of \sqrt{1727} is 1727.

$$\frac{\sqrt{25931}\sqrt{1727}}{90\times 1727}$$

To multiply \sqrt{25931} and \sqrt{1727}, multiply the numbers under the square root.

$$\frac{\sqrt{44782837}}{90\times 1727}$$

Multiply 90 and 1727 to get 155430.

$$\frac{\sqrt{44782837}}{155430}$$